Mathematical modeling and computer simulations will be used to study lymphocyte repertoire dynamics. Specific objects of study will be the degree of stochasticity in antigen receptor gene rearrangement and the interaction of this process with lymphocyte selection; the dynamic parameters governing clonal selection of lymphocytes; models for the receptor-ligand interactions underlying the dynamics of lymphocyte selection and differentiation; and the dynamics of hypermutation and affinity maturation. Models will be used to test hypotheses aimed at reconciling the findings on the continuous nature of antigen receptor gene rearrangement with the allelic exclusion paradigm; the paradoxes of self-restriction and alloreactivity; and the apparent contradiction between the affinity maturation paradigm and B cell repertoire shift. Throughout these studies, models will be used to study possible mechanisms for the breakdown of tolerance (central or peripheral) leading to autoimmune disease.